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From a sample of 109 candidate Ultra-Strong Mg II (USMgII; having restequivalent width of Mg II absorption, $W_{2796}>3.0$ Angstrom) systems atz=0.4-0.6, we confirm 27 and identify host galaxies of 20 systems based onassociated nebular line emission from our SALT observations or from SDSS fiberspectra. The measured impact parameter, [O II] luminosity, star formation rate,B-band luminosity and stellar mass are in the ranges $7.3\le D[kpc]\le79$,$0.2\le L_{[O II]}[ 10^{41}~erg s^{-1}]$ $\le 4.5$, $2.59\le SFR[M_\odotyr^{-1} ]\le 33.51$, $0.15L_B^*\le L_B\le1.63L_B^*$ and $10.21\lelog[M_*/M_\odot]\le11.62$ respectively. The impact parameters found are largerthan that predicted by the $W_{2796}$ vs D relationship of the generalpopulation of Mg II absorbers. At a given D, USMgII host galaxies are moreluminous and massive compared to typical Mg II absorbers. However, the measuredSFRs are slightly lower than that of main-sequence galaxies with the sameM$_\star$ at $z\sim0.5$. We report a correlation between $L_{[O II]}$ andW$_{2796}$ for the full population of Mg II absorbers, driven mainly by thehost galaxies of weak Mg II absorbers that tend to have low $L_{[O II]}$ andlarge impact parameters. We find at least $\sim$33% of the USMgII host galaxies(with a limiting magnitude of $m_r<23.6$) are isolated and the large $W_{2796}$in these cases may originate from gas flows (infall/outflow) in single halos ofmassive but not starburst galaxies. We also find galaxy interactions could beresponsible for large velocity widths in at least $\sim$17% cases.

Host Galaxies of Ultra Strong Mg II absorbers at z $\sim$ 0.5